The post Open House: Wednesday, June 5th appeared first on Talking Stick Learning Center.

]]>Stop by to talk to staff and participants about our programs for homeschoolers ages 4-17. We will be hosting the entire open house at our Garden Classroom. We have several families attending with young people in different age groups, so we are planning to have all ages, all programs meet in one location.

To let us know that you are going to attend, please click here.

And please share this with any families you think might be interested in Talking Stick!

**DATE:** Wednesday, June 5th, 2019**TIME:** 10:00 a.m. to 12:00 p.m.**LOCATION:** The Garden Classroom at Awbury Arboretum

The Garden Classroom is accessible by foot through the entrance on Ardleigh Street, northwest of Washington Lane. Please park on Ardleigh St and walk up the path across from E. Duval Street to the green classroom building.

Directions to the Garden Classroom

*Please note that other directions or GPS to Awbury Arboretum will take you to Cope House, which is NOT walking distance to the Garden Classroom.*

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]]>The post Teen Open House: Monday, February 25 appeared first on Talking Stick Learning Center.

]]>Stop by to talk to staff and participants about our programs for homeschoolers ages 13-17. We will be hosting the entire open house at our Garden Classroom. This Open House will take place during regular programming so you have a unique chance to engage directly with facilitators and participants.

To let us know that you are going to attend, please click here.

And please share this with any families you think might be interested in Talking Stick!

**DATE:** Monday, February 25th, 2019**TIME:** 12:00 p.m. to 3:00 p.m.**LOCATION:** The Garden Classroom at Awbury Arboretum

The Garden Classroom is accessible by foot through the entrance on Ardleigh Street, northwest of Washington Lane. Please park on Ardleigh St and walk up the path across from E. Duval Street to the green classroom building.

Directions to the Garden Classroom

*Please note that other directions or GPS to Awbury Arboretum will take you to Cope House, which is NOT walking distance to the Garden Classroom.*

The post Teen Open House: Monday, February 25 appeared first on Talking Stick Learning Center.

]]>The post Open House: Wednesday, January 9th appeared first on Talking Stick Learning Center.

]]>Stop by to talk to staff and participants about our programs for homeschoolers ages 4-17. We will be hosting the entire open house at our Garden Classroom. We have several families attending with young people in different age groups, so we are planning to have all ages, all programs meet in one location.

To let us know that you are going to attend, please click here.

And please share this with any families you think might be interested in Talking Stick!

**DATE:** Wednesday, January 9th, 2018**TIME:** 10:00 a.m. to 12:00 p.m.**LOCATION:** The Garden Classroom at Awbury Arboretum

The Garden Classroom is accessible by foot through the entrance on Ardleigh Street, northwest of Washington Lane. Please park on Ardleigh St and walk up the path across from E. Duval Street to the green classroom building.

Directions to the Garden Classroom

*Please note that other directions or GPS to Awbury Arboretum will take you to Cope House, which is NOT walking distance to the Garden Classroom.*

The post Open House: Wednesday, January 9th appeared first on Talking Stick Learning Center.

]]>The post Category Theory #2: Grappling with Abstraction appeared first on Talking Stick Learning Center.

]]>“No, Penelope is not a pig. She is a pig *puppet*. There’s a big difference,” I replied as we sat down. This seemingly inane comment of mine captured everyone’s attention.

** **

**PIG-PUPPET YEARS**

“You know how it is said that a year for humans is like 7 for dogs and 5 for cats?” I asked? Everyone nodded.

“There are also fox years,” added A.

“Yes, and there are pig-puppet years. But they work in the opposite direction as dog years and cat years. For every 10 years that a human ages, a pig puppet only ages 1 year. So even though I got Penelope almost 30 years ago, her age is really 3.”* We discussed this concept for a moment, and then I announced, “I’m having some trouble with Penelope that you can probably help me with. I’m trying to teach her about numbers, but listen to how she responds to my lessons:”

Me to Penelope the pig puppet: “If Grandma gives you five cookies and Grandpa gives you five cookies, how many cookies will you have?”

Penelope to me: “None, because I’ll eat them all!”**

** **

**DOES CONTEXT MATTER?**

Penelope’s statement set off a huge mathematical conversation. Students had questions and comments about what numbers are, how to explain them, what counting really means, the difference between numbers and numerals, and how numbers first came into being. We talked about all of these things, and then returned to the original scenario. The students tried and tried to teach Penelope the math problem above by changing the context:

Student: “What do you get when you combine five blobs and five blobs?”

Penelope: “One, since blobs squish together when you combine them!”

Student: “What do you get when you combine five pieces of titanium and five pieces of titanium?”

Penelope: “One, since titanium is a metal and metals melt at high temperatures.”

Student: “What do you get when you combine five wooden blocks and five wooden blocks?”

Penelope: “Zero, because I like to play with matches!”

Student: “What do you get when you combine the numeral five and the numeral five?”

Penelope: “Fifty-five, since the fives are right next to each other now!”

Turns out that no matter what context the students came up with (probably 20 examples in all), Penelope had a way to make the problem not work. No matter what, five things plus five things didn’t equal ten.

A: “How can Penelope know so much about other things and not know anything about math?”

Me: “She’s a science prodigy.”

F: “But aren’t math and science related?”

Me: “Yes, but that’s another thing that’s special about pig puppets. We can take some creative liberties.”

By this time, the puppet Penelope had somehow moved from my hand to F’s hand, and the students had taken over both roles – coming up with new contexts and finding ways to contradict the hoped-for result. No one was able to come up with a context that Penelope (in most cases actually M) couldn’t knock down. I was just enjoying the show.

** **

**STRIPPING AWAY CONTEXT**

“What’s the difference between the problem *five plus five equals ten* and the problem *five things plus five things equals ten things*? I asked. The students’ thinking even further intensified. They posited conjectures, debated them, rejected them until S*** said “My brain hurts!” The others agreed.

“What’s the difference between numbers and things?” I asked more directly.

“Well, numbers are something that we made up to talk about things,” answered A.***

“Do numbers exist as things in the natural world?” I asked.

“Yes,” said about half the students.

“No,” said the other half at the same time.

They all looked at each other. Then those that said Yes changed their answers to No.

“Are they ideas?” I asked.

“Yes!” everyone agreed. We talked about ideas versus things. How mathematicians use the word abstract to describe ideas that can then be applied to multiple scenarios.

“Like abstract art,” said S excitedly. Then she quickly reversed herself: “Actually, no, since abstract art is a thing.”

“My brain really hurts now,” said A.

“Do cookies behave logically?” I asked?

“No. People eat them!”

“So would mathematicians rather study things that behave logically or things that do not?” The students all agreed that “logical things” is the answer. I explained that mathematicians like to strip away the context to get at the underlying abstract structure of things. This can reveal similarities, I continued, like in that problem we did last week with the symmetries and arrangements.

But is it always mathematically sound to strip away all context? If a problem is totally abstract, will you arrive at a useful answer?

**RECONSIDERING CONTEXT**

I presented the students a paraphrase of a problem from Eugenia Cheng’s book __How to Bake ____π__:****

*You run a company that takes people on tours. You’re organizing a trip for 100 people.* *You’re renting minibuses and want to maximize your profit. Each minibus holds 15 people. How many do you have to rent?*

The students started out by trying numbers: 10 busses – too many. 9 busses – still too many. Then S suggested dividing 100 by 15, yielding 6.6̅. After some discussion, they concluded that we need to rent 7 busses, so 100 ÷ 15 = 7.

“That’s it? That’s the problem?” said S, a bit disappointed. She was happy to hear that no, that’s just the first part. The problem continues:

*Now you’re shipping some chocolates to a friend. You pre-paid for a stamp that covers the cost of mailing 100 ounces. Each chocolate weighs 15 ounces.* *How many pieces can you send to your friend without paying extra for shipping?*

Immediately the students saw that it’s the same calculation but a different interpretation of 6. 6̅. They all were talking but not so much to each other or me. More like each was thinking aloud, simultaneously. S persevered the longest and gave a solid explanation of why in this case, 100 ÷ 15 = 6.

“So here’s the real problem,” I said to the students. *“Why is the answer 6 when you’re talking about chocolates and stamps but the answer 7 when you’re talking about people and busses?”*

“Context matters,” they all agreed. I quoted Cheng to them: “Be careful not to throw away too much… Category theory brings context to the forefront.”

“What would be the answer,” I asked, “to a person who looked at this problem purely abstractly, with all of the context stripped away?”

“6. 6̅” they all agreed. They definitely were grasping abstraction versus reality and some key points about context. But it was time for a break. People’s brains had started hurting 20 minutes ago.

** **

**FUNCTION MACHINES AND CAKE CUTTING**

I gave everyone an apparent brain break by doing a function machine with them. (The students provide a number that goes “in,” I tell them what number comes “out,” and their job is to discern the rule.)

“Now try this one: If you slice a cake, what’s the function for the maximum number of pieces you can get with a certain number of cuts?” (I also worded it in the language of circles at F’s request: “What is the function for the maximum number of regions you can create with a certain number of chords in a circle?”)

I started sketching this on the board with the students’ verbal instructions (“2 pieces from 1 cut, 4 pieces from 2 cuts,” etc.). But almost immediately, the students were all at the board figuring it out for themselves. Once again, I sat back and enjoyed. Most of the students quickly got 7 pieces from 3 cuts.

“I got 10 pieces from 4 cuts,” announced M.

“Can you get more?” I asked. She tried, without success, and then went on to test 5 cuts and 6 cuts. By then, at least three students had diagrams with 10 pieces from 4 cuts. “You can get more,” I promised. “There’s something that all of you are doing that you could change to get more.” They kept working.

“Can you get more than 7 pieces from 3 cuts?” backtracked S.

“No one ever has,” I said.

“But just because no one ever has, does that mean it can’t be done?” she asked. “Has anyone demonstrated that it definitely can’t be done?”

“That is one of the key questions in mathematics,” I said, so excited by this question. A huge goal of our math circle is to teach kids to be doubters. “In math, it’s not enough that no one has ever done something. There has to be a proof that it can’t (or can) be done for us to believe anything. And yes, there is a proof that you cannot do more than 7.”

“I got 11!” announced A, who had been fervently trying to beat the class record of 10 from 4 cuts.

“Now you’ve reached the number that has been proven to be the maximum.”

My intended point of this activity had been to look for a pattern/function/rule to determine the number of slices. We had a nice sequence of numbers (2,4,7,11), but no one was interested in pattern-seeking. They just wanted to keep testing. So I played the big-number card: “How many pieces could you get from 500 cuts?”

“We would need bigger whiteboards and more markers,” said someone, defeating my attempt to redirect the approach.

I played the ridiculous-number card: “If you had to determine how many pieces you could get from 5,000 cuts, would you rather have a bigger whiteboard or know the rule?” Someone grudgingly said that the rule would be better in that case, but it didn’t detract from anyone’s enthusiasm for drawing.

We were out of time. Had we gotten to the point where students showed interest in determining a rule, I would have burst their bubble anyway with some talk about how patterns don’t mean rules without a proof. (Again, training doubters.) So we ended on a high note with me connecting this activity to the idea of abstraction.

**A FEW OTHER THINGS**

Early in the session, the students brought up the golden goose problem from last week. (*Would you rather have golden eggs, a goose that makes golden eggs, a machine that makes those geese, or a machine that makes those machines?*) Some students had talked about it at home and were reconsidering their answers from last time. We talked about the levels of knowledge you needed for each item in this hierarchy, and how that ties to mathematics. The students wanted to explore whether the answer to the question would be different if we removed the goose as a possibility. I explained that “What would happen if we changed the question a bit?” is exactly something mathematicians ask all the time. This came up later in the class, when S was doing the cake-cutting problem without realizing that the cuts had to be chords, not just random line segments. She made a quick shift from initial disappointment that she had misunderstood the problem to excitement to hear that this might a new way to do this problem that people hadn’t worked on before.

Rodi

*I’m relaying this anecdote so that interested parents can have a jumping-off point to talk more about ratios and proportions at home.

** Eugenia Cheng, __How to Bake ____π__, p19. We also dramatized with Penelope the pig puppet Cheng’s examples of the difference between having memorized the sequence of counting numbers and actually understanding what they mean. (p20) Cheng discusses the cake-cutting problem on pages 33-34. You can find an algebraic explanation of the problem on Wolfram MathWorld and many other places. It’s a classic problem.

***We have two students whose names begin with S, and I’m using S for both. Ditto for A.

****Cheng, p21

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]]>The post Category Theory 1: Odd One Out appeared first on Talking Stick Learning Center.

]]>ODD ONE OUT

The students found it easy to conclude that the grey duck was the odd one out when all the others were yellow and every other attribute was identical. But what to do when multiple attributes change? After vigorous debate over some pre-determined groups of objects,* the students created their own odd-one-out challenges for each other. They used markers, cubes, pentominoes, playing cards, shape tiles, and rocks.

“Even though this one is the odd one out because of color, you’re wrong. A different one is the odd one out.”

“You’re right that this one is the odd one out, but your reason is wrong.”

Again and again, students stated versions of the above two comments. Serious mathematical discoveries were going on here:

- Changing assumptions changes the answer.
- There can be multiple paths from beginning to end.
- You have to state your reasoning or your conclusion won’t stand up to scrutiny.

Soon, the students changed the wording of their replies:

“You’re right that this one is the odd one out because of color, but that’s not what I had in mind. I was thinking that a different one is the odd one out.”

“You’re right that I was thinking that this one is the odd one out, but your reason is not the reason that I was thinking.”

Do you see the significance of the change in wording?

PROOFS

The students were essentially creating physical proofs, except that here, the conclusion/proposition wasn’t stated at the beginning as it is in a mathematical proof. You could say that the students created the building blocks of mathematical proofs. To paraphrase mathematician Eugenia Cheng,** proofs are like storytelling with a beginning, middle, and end. In the beginning you state your assumptions and definitions. In the middle you state your reasoning. In the end, you state your conclusion (i.e. “ta-da!”). In our group, the beginning, middle, and end of the proof emerged through asking questions, positing conjectures, rejecting or accepting conjectures, and then finally a statement of the author’s reasoning.

The students proved that “this one is the odd one out because it is the only one that”

- is a non-primary color.
- has the white cubes totally enclosed in a boundary.
- doesn’t start with the letter B.
- has no symmetry.
- has no other objects in the group that share a shape.
- has a rough texture.
- has writing of a slightly thicker font.
- etc., etc., etc.

No one set up a group where the obvious attribute (color, size, etc.) was the exception. The exceptional attributes were hidden. Just like in an interesting math problem! I expected this activity to take 5-10 minutes, but it took much longer. I had set an alarm to give us a three-minute break after 50 minutes. When that went off, A said, “Wow, Math Circle goes fast!” It felt like we had just gotten started. We could have done this activity all day. Even when we moved on to other activities, the students took odd-one-out interludes to continue challenging each other.

ABSTRACTION

Another aim of category theory is abstraction – seeking the underlying structure of things in a way that allows you to see a similar structure in seemingly very different things. By “things” I mean mathematical things. By “mathematical things,” I mean things that have a logical structure. I have seen Cheng extend “things” to non-mathematical things. She applies category theory to real life. I hope to do this later in the course, but for now we’re sticking to logical things.

We explored Cheng’s juxtaposition of the symmetries of equilateral triangles to permutations of the numbers 1,2, and 3.*** It may have seemed like this was an activity about properties of triangles, types of symmetries, and one way to calculate a permutation (listing it out). The students did conclude that an equilateral triangle has 6 symmetries and a list of three digits has 6 permutations. But the big question was this: is that just a coincidence? Or (dramatic music here) *could they really be the same problem*?

One thing I love about doing “high-level” math with younger students (here, ages 10-12) is that they are not blinded by too many preconceived notions about math. (Of course, they’re blinded by some. I see five-year-old students convinced that any problem that’s not about number theory is not mathematics and that there’s only one right answer no matter what and that every question has an answer and that the teacher knows it and that there’s only one way to get the answer and and and…. Okay, I’ll get off my soapbox now.)

“Of course, it’s the same problem,” S right away announced. The others quickly agreed with her. We talked briefly about how the underlying structure of things can be the same despite the obvious differences. This idea blew my mind when I first encountered it at an age much older than these students. I suspect that at least some older students might think it’s just a coincidence.

I put “high-level” in quotes because category theory is generally not taught to students before graduate school or possibly third-fourth year college. Cheng is leading a movement to make it accessible to middle- and high-school students. Math Circles in general are hoping to make deep mathematical study accessible to younger and younger students.

GOLDEN EGGS

In our last few minutes, we played an informal round of Would You Rather:

- Would you rather have some golden eggs, or a goose that lays golden eggs?
- Would you rather have a goose that lays golden eggs, or a machine that makes geese that lay golden eggs?
- Would you rather have a machine that makes these geese, or a machine that makes machines that make these machines?

This discussion was rich, going off in many philosophical and mathematical directions. Cheng gives this example**** to make a point about abstraction: “in order to build a machine to do something rather than doing it yourself, you have to understand that thing at a different level.” You have to analyze every step and every implication of those steps. This is some of the thinking we do when our goal is abstraction. We were out of time at this point, so never really did get to a discussion about this perspective. We’ll start there next week.

All of this in 75 minutes – phew! Fortunately, we have five more weeks.

Rodi

*Here are the puzzles on paper that the students debated:

http://www.puzzlesandriddles.com/WordPuzzle15.html

https://twominfun.com/odd-one-out-puzzle/odd-one-out-5/

** __How to Bake ____π__ , Eugenia Cheng, pp66-68

*** Cheng, p17

**** Cheng, p31

The post Category Theory 1: Odd One Out appeared first on Talking Stick Learning Center.

]]>The post “Waggy, Do You Eat Meat?” (Some Basic Tenets of Mathematics) appeared first on Talking Stick Learning Center.

]]>*On a particular island, every inhabitant (puppet) is either a knight, who always tells the truth, or a liar, who always lies. Which puppet is a liar? Which one a knight? You can either listen to their statements, or ask them questions.*

“What’s a statement?” asked A immediately. And our first session was off and running.*

Some deep mathematical thinking beyond the questions of what is a statement, what is the opposite of a statement, and how can you categorize things as statements and their opposites came up:

**Subjective versus objective:** When the students asked the puppets questions, they discovered that some questions did not clarify matters: “Baby Puppy, are your ears floppy?” “Kitty, do you like milk?” “Waggy, is your tail pink?” all resulted in answers that gave different students different conjectures. When the puppet Penelope said “my tail is strong,” the students thought this was a clear indicator of a liar until after the round, when Penelope demonstrated how her skinny short tail could lift an object. The students figured out that words like floppy, like, pink, and strong are subject to interpretation. They learned to use words that leave less room for interpretation to arrive at an answer sooner: “Rooney, do you have two ears?” “Cat, do you have a tail?” While you can certainly argue that there are multiple interpretations of two and ears, we were headed in the direction of precision, one of the basic tenets of mathematics.

**Precision:** When we introduced puppets/characters that sometimes tell the truth and sometimes lie (normals), things got trickier. One puppet told 11 lies then a truth. Another told 8 truths then a lie. The students disagreed on how to categorize them. A identified them as normals. N identified them as a knight and a liar, respectively. They both agreed that a puppet who told half truths and half lies was a normal. A held firm that one exception eliminates a puppet from a category. N argued the definition of the word “sometimes:” a pattern with just one exception does not count as “sometimes.” She felt that “sometimes” was not well-defined. Neither student was able to bring the other around to the other position, but they did both agree that had we been given 5 categories instead of 3 that their answers would then be the same. I forget to mention that these students are just six years old!**

**Functions**: “Waggy, do you eat meat?” Waggy said no. “But he’s a fox and foxes eat meat,” said one of the students,“so he must be a liar.” “But everything else he said was the truth,” said the other.*** They debated this, asked many more clarifying questions, and finally decided that Waggy was a knight despite the meat thing. I explained afterwards that Waggy is really a puppet/actor who was playing the role of a fox but really lives in a bag in my closet and eats nothing. (In my mind, this idea is like nesting dolls or even compound functions, where one function is processed through another before an answer is obtained.) Once the students realized this, it made the game both more complicated and clear at the same time.

**Certainty/Proof**: *If we clarify the word “always” from the original question to mean “with no exceptions,” how many questions do we have to ask the puppets to be certain of their categories? *This question was confusing to the students. (They’re just six years old, after all.) They had various conjectures, all of which were a single number. One student said 16. “So what if that puppet told the truth 16 times, and on the 17^{th} statement or question, told a lie?” I asked. At this point, it was clear that the students’ brains were fried. (Fortunately, I hadn’t gone so far that they got discouraged/frustration.) I had lost track of time. We had been doing math for an hour and twenty minutes. So I sent them home.

**Ownership**: One goal of our Math Circle is for students to own the mathematics, for the facilitator to ideally be a fly on the wall. In the second week of class, A attended, N did not, and a group of new students (ages 5-7) were there. I asked A if she wanted to demonstrate/teach the game of Knights and Liars to the others. She wanted to and she did.

Note for families of new Math Circle participants: I was recently asked what opening activity I like to do for a new course. Here’s what I said. At the Talking Stick Math Circle, we like for the students to have an immediate immersion into mathematical thinking. So whatever problem we take on, we start using the terms "conjecture," "proof," "question," "mathematician," the phrase "I don't know," and for older students the word "assumption" right from the start. This gives many of our students a sharp contrast to some of their other math experiences, and hopefully the beginning of an understanding of what mathematics is. I purposely pose questions that I don't know the answer to. I use the above terms without defining them (until someone asks). Our goal is that eventually (over weeks or months or even years), students will discover the difference between inductive and deductive reasoning. With older students, we talk about that right from the start. Another term important to mention right from the start is "collaboration." I like to give a problem that's pretty impossible for a single students to figure out, but is solvable by a group. Then we talk about how the problem got solved collaboratively.

Rodi

*You can read more about how the game is played from Smullyan’s book “What is the Name of this Book?” or from my reports about this game from another session five years ago: https://talkingsticklearningcenter.org/logic-session-2-knights-liars-percy-jackson/

**I am paraphrasing some of the mathematical language that the students used, but not changing their meaning at all.

***Only 2 students attended the first session. I invited parents and siblings to round out the group, but it turned out that wasn’t necessary.

The post “Waggy, Do You Eat Meat?” (Some Basic Tenets of Mathematics) appeared first on Talking Stick Learning Center.

]]>The post Open House: Wednesday, September 12 appeared first on Talking Stick Learning Center.

]]>Stop by to talk to staff and participants about our programs for homeschoolers ages 4-17. We will be hosting the entire open house at our Garden Classroom. We have several families attending with young people in different age groups, so we are planning to have all ages, all programs meet in one location.

To let us know that you are going to attend, please click here.

And please share this with any families you think might be interested in Talking Stick!

**DATE:** Wednesday, September 12th, 2018

**TIME:** 10:00 a.m. to 12:00 p.m.

**LOCATION:** The Garden Classroom at Awbury Arboretum

Directions to the Garden Classroom

The post Open House: Wednesday, September 12 appeared first on Talking Stick Learning Center.

]]>The post New Math Circle Course Schedules appeared first on Talking Stick Learning Center.

]]>**Unofficial schedule**

__Classic Math Circle Problems__

Dates: Thursdays, 3:30-4:30pm, 9/20-10/18 (5 weeks)

Suggested Ages: 5-7

Knights and Liars, open questions, story problems, pattern making and breaking, explorations of infinity, proofs, and more. We will have fun with these classic math circle activities as students develop the mathematical-thinking skills of asking questions, forming conjectures, testing conjectures, and generally seeking the underlying structure of things.

__ __

__Category Theory__

Dates: Thursdays, 3:30-4:45pm, 10/25-12/6 (6 weeks, 75-minute sessions, 7.5 hours total, no class on Thanksgiving)

Suggested Ages: 10-14

Mathematician Eugenia Cheng describes category theory as “the mathematics of mathematics.” Inspired by Cheng’s book “How to Bake Pi,” we will do activities that use abstract mathematics to see, understand, and generalize the defining structure of things. And by “things” I mean mathematical things, logical things, and social phenomena. Visit her website (eugeniacheng.com) for a preview.

__Queen Dido Problems__

Dates: Thursdays, 3:30-4:45pm, 1/24-3/21 (8 weeks, 75-minute sessions, 10 hours total, no class on 3/7)

Suggested Ages: 13+

In this course, students will explore real mathematics problems from ancient history. These will include Queen Dido problems, Zeno’s Paradox, and ancient inheritance problems. We’ll do the math and put the problems in their historical contexts. We may dabble in a few mythological problems as well. Mathematical concepts will include pre-algebra, algebra, geometry, and some calculus, but pre-requisite knowledge of these topics is not required.

__Polyominoes and Functions__

Dates: Thursdays, 3:30-4:30pm, 4/4-5/16 (6 weeks)

Suggested Ages: 8-10

Polyominoes are a hands-on geometry activity that develop students’ thinking about classification, combinatorics, symmetry, and more. We will also study characteristics of functions via the book Funville Adventures (or via extensions of this book if the students have already used it) and function machines in order to develop algebraic reasoning skills.

(registration information should be posted within a week)

The post New Math Circle Course Schedules appeared first on Talking Stick Learning Center.

]]>The post Open House: Thursday, May 31, 2018 appeared first on Talking Stick Learning Center.

]]>To let us know that you are going to attend, please click here.

And please share this with any families you think might be interested in Talking Stick!

**DATE:** Thursday, May 31st, 2018

**TIME:** 10:00 a.m. to 12:00 p.m.

**LOCATION:** The Garden Classroom at Awbury Arboretum

Directions to the Garden Classroom

The post Open House: Thursday, May 31, 2018 appeared first on Talking Stick Learning Center.

]]>The post Learning Survival Skills with My Side of the Mountain appeared first on Talking Stick Learning Center.

]]>The first week we sewed bags for foraging supplies. Sam made himself clothes and bags for gathering from deerskin that he tanned. We made ours from fabric, hand sewn, so we could go out and collect acorns and other things on our walks. Early in the fall, we went for a foraging walk around Awbury Arboretum, identifying some of the plants Sam used in the book, sassafras for tea, cattails for flour. I showed them how to identify poison ivy, and also jewelweed, which can be rubbed on skin that has been exposed to poison ivy and stinging nettles. And most important of all, we collected acorns to make the pancakes. This became an obsession with our group, each week they would say “when can we make acorn pancakes like the ones Sam ate in the book?”.

Then began the very long process of prepping the acorns to make flour to make the pancakes. First, the acorns had to be cracked open. They did it with hammers and mallets and rocks. All those acorns we had collected didn’t look like as much when we just had the nut meat. Various days through the fall they worked on cracking open the nuts, just that was a lot of work. I did some research and read that if you boil and rinse the acorns several times, it takes some of the tannin out and makes them less bitter. I did this at home, we just don’t have enough time during our days to do all this prep. We had talked about the tannin and the flavor of the acorns, and that the consistency of Sam’s pancakes would be more like a tortilla than the fluffy pancakes we are used to. None of this lessened their enthusiasm about making pancakes. Also, I told them I would bring some modern pancake batter and we would have both. Finally, in November, it was pancake day. First, we had to grind the nut meat into flour. We did it between rocks like Sam did in the book. The pictures show the tiny bits of acorn dust they were getting from grinding, and then the two little pancakes we made. No worries, no one liked them anyway and we had plenty of present day pancakes to eat.

Three different weeks during the fall we worked on lighting a fire with a flint and steel. One survival skill I learned was that having the right tinder is very important. In my trial run before doing it with the young people, I just lucked into finding great tinder, so I assumed if we just picked some dry grass at Awbury it would work. But when we collected tinder at Talking Stick, everyone struggled the first time to get it to keep burning, the dried grass we found just didn’t light as easily. But even with the struggle, it was fun figuring out how to get a spark, then a little flame. The second and third time I brought dryer lint for them to use as tinder, definitely cheating, Sam didn’t have lint out in the woods. But with the lint we all succeeded lighting fires, by the third time out everyone could light a small fire.

One thing that really helped Sam survive was that he caught a young peregrine falcon, named her Frightful, trained her and taught her to catch meat for him. In class, we talked about raptors and watched videos of them in flight and hunting. I planned a field trip to go to Militia Hill to their Hawk Watch to see hawks migrating and learn about raptors from their volunteers. Unknown to me, one of their volunteers is a licensed falconer and has a pet peregrine falcon that he would bring for us all to see. That field trip was a great day, we had beautiful weather. It was the very end of the migration season, so we didn’t see a lot of raptors, but the volunteers told us a lot and answered our questions. Getting to see Cleo the falcon up close was so exciting.

Tom told us all about her, her story, what is involved in training and taking care of a falcon.

My Side of the Mountain has always been a favorite book of mine, I read it several times when I was young and then again to our children. It was great to take it to another level, to actually learning some of the survival skills that Sam used with the young people at Talking Stick. It certainly made an impression on me, the amount of work that goes into each thing he did, making his own clothes from deer hide, making acorn pancakes, lighting fires, training a falcon. I loved their enthusiasm for both the book and the projects, each week they would come running in saying, ”what are we doing today?”.

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